Formal Concept Analysis and Structures Underlying Quantum Logics [chapter]

Ondrej Krídlo, Manuel Ojeda-Aciego
2018 Communications in Computer and Information Science  
A Hilbert space H induces a formal context, the Hilbert formal context H, whose associated concept lattice is isomorphic to the lattice of closed subspaces of H. This set of closed subspaces, denoted C(H), is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called "propositional system", that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by
more » ... ucing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of ChuCorsH of Chu correspondences between Hilbert contexts.
doi:10.1007/978-3-319-91473-2_49 fatcat:rjwuwor6jnbtdgwmn4iz63tmha